Help me please please

F(x) = x2 – 3x – 2 is shifted 4 units left. The result is g(x). What is g(x)?

Ray Of Light [21]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now... your expression is not in vertex form, that's ok... to do a horizontal shift to the left by 4 units, we can simply, add the C and B component to the "x" variable, C=4, B =1, that way the horizontal shift of C/B or 4/1 is just +4, giving us a horizontal shift to the left

$\bf f(x)=x^2-3x-2\impliedby \textit{let's change that for }f(1x+4)
\\\\\\
f(1x+4)=(1x+4)^2-3(1x+4)-2
\\\\\\
f(x+4)=x^2+8x+16-3x-12-2
\\\\\\
f(x+4)=x^2-5x+2\impliedby g(x)$

8 0

3 years ago

Read 2 more answers

Helppppppp pleaseee

Viktor [21]

Answer:

$x=2\sqrt{5}$

Step-by-step explanation:

If that is a square, then all sides are the same. Therefore, it's a $\sqrt{10}$ by $\sqrt{10}$ shape. We'll use Pythagorean Theorem to find the diagonal.

$a^2+b^2=c^2\\\sqrt{10}^2+ \sqrt{10}^2=x^2\\10+10=x^2\\20=x^2\\\sqrt{20}=x\\\sqrt{4*5}=x\\ 2\sqrt{5}=x$

Since it's not a fraction, there is no denominator to rationalize. Let me know if you have any other questions!

5 0

2 years ago

93 is the sum of a number g and 58

Wewaii [24]

Assuming you are hoping to obtain the value of "g", to solve worded algebra problems like these, it is easier to translate the world problem into a mathematical equation first.

In this case, "93 is the sum of a number g and 58" can be translated to:

93 = g + 58

To find the value of g, it is necessary to isolate g first. To do this, we subtract both sides of the equation by 58:

93 - 58 = g + 58 - 58
93 - 58 = g

Simplifying:
g = 35

5 0

3 years ago

Read 2 more answers

Which statement is true?

seropon [69]

Answer: C. A line that rises from left to right has a positive slope.

Step-by-step explanation: A. has a slope of 0, B. has an undefined slope, and D. is supposed to go left to right not right to left.

6 0

3 years ago

Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ . However, it is not suff

Fittoniya [83]

Answer:

direction

shape

scatter plots

shape and outliers

Step-by-step explanation:

Correlation is defined as the degree of correspondence between two variables.

When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .

Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of scatter plots can provide other helpful details such as shape and outliers

5 0

3 years ago